961 Hi Yvonne, I wouldn’t consider this really an aggression or training problem. It really is just normal and expected behavior. This is why many carefully managed dog parks do not allow unspayed adult dogs or toys inside.
In general the herding breeds do not do as well as adults in these situations as the sporting breeds such as labs, goldens, etc.. that were selectively bred to remain more juvenile in nature and not as defensive about objects or personal space. This is all part of just knowing that different breeds have different tendencies. So if someone wants to have a dog for dog park activities and socialization you choose sporting breeds, and if someone wants a dog that can double as part of a security plan you choose a German Shepherd, Rottweiler etc..
This does not mean that your girl cannot socialize and play at the beach, but you will have more issues as she matures with new dogs, especially other females if she is left intact (and less so if she is spayed). You need to be wary of the personalities of new dogs since more assertive dogs may push her buttons too quick and there is a possibility of scrap. This can even happen in puppy classes, but always bigger problem with adult dogs and adult teeth.
Bringing her toy their is also looking for trouble unless the toy is YOURS and you are playing with her. If in her mind it is HER toy, now she has something to worry about and guard when she is unsure of the intentions of other dogs that want to claim it as theirs’. That is just the nature of the dog. Again, I don’t even allow dog toys to be part of the socialization process in puppy classes. Toys and people handing treats to all the dogs/puppies in loose dog situations are common reasons for conflict as it gives something valuable to compete over. Most normal “dog play” is practice hunting and practice fighting on each other. Possessions and resources thrown into the mix can cause “real fighting” if the dogs are not well established in their relationship and secure with their roles. Usually it is easier to just remove the possessions from the equation.
I do small scale breeding of German Shepherds for working purposes..personal protection and police. None of them would do well in a dog park setting after maturity, just like I wouldn’t do well in a playground meant for adults and having random men want to wrestle with me. As she matures will become more of an “inner circle” dog rather than the social butterflies that the less mature dogs often are. 18 to 24 months you start seeing more obvious changes. Puppyhood is fleeting with the working breeds, especially when intact.